More than 100,000 Christians gathered at the site in Anambra state early Saturday for All Saints' Day and the first day of the month, Leadership Newspapers reported.
Witnesses said a group of people began shouting "fire," causing a panic.
The injured were transported to local hospitals for treatment.
Gov. Peter Obi, who later visited the injured at the hospitals, vowed to open an investigation into the stampede, The Punch, Nigeria, reported.
Leadership newspapers said there was speculation that the stampede was set off by Obi's political opponents. The governor had left the prayer site before the chaos broke out, the newspaper said.
2013: Top 11 Bacon stories of the year!
Nativity scenes to be moved at Guantanamo after troops' protest